c
Let \(l\) be the length of block immersed in liquid as shown in the figure. When the block is floating,

\(\therefore \quad m g=A l \rho m\)

If the block is given vertical displacement \(y\) then the effective restoring force is

\(F =-[A(l+y) \rho g-m g]=-[A(l+y) \rho g-A l \rho g] \)

\(=-A l \rho g y\)

\(Restoring\, force =-[A l \rho g] y .\) As this \(F\) is directed towards its equilibrium position of block, so if the block is left free, it will execute simple harmonic motion. \(Here\, inertia\, factor = mass \,of \,block =m\) 

\(Spring ,factor =A \rho g\)

\(\therefore \quad\) Time period \(=T=2 \pi \sqrt{\frac{m}{A \rho g}}\) i.e. \(T \propto \frac{1}{\sqrt{A}}\)